Some Exact Solutions in Nonlinear Oscillations
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概要
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Forced oscillations of systems with nonlinear restoring forces are treated rigorously in certain special cases which are specified by the condition that the harmonic oscillation has a similar wave form to that of the external force. From this condition we are led to the introduction of the external force represented by the function cn for a hard system and by the function sn in the case of a soft system, and consequently the solution is given by either of these functions. Response curves obtained are similar to the corresponding response curves which have been given by approximate solutions. To examine the stability of the- forced oscillation one must. solve Hill's equations, which can be carried out exactly in the present cases. Thus, the stable or unstable regions in the response diagrams are determined definitely and a few questions are clarified.
- 社団法人日本物理学会の論文
- 1952-08-25